The present invention relates to a method for achieving ultrahigh recording density by use of multi-stable vortex states discovered in ferroelectric nanostructures.
Bulk ferroelectrics undergo structural phase transformations at low temperatures, giving multi-stable (that is, multiple-minimum) degenerate states with spontaneous polarization. Accessing these states by applying, and varying the direction of, an external electric field is a key principle for the operation of devices such as non-volatile ferroelectric random access memories (NFERAMSs) [10]. Interestingly, these properties can dramatically change when going from bulks to nanostructures [50-52]. Compared with bulk ferroelectrics, low-dimensional finite ferroelectric structures promise to increase the storage density of NFERAMs 10,000-fold [8]. But this anticipated benefit hinges on whether phase transitions and multi-stable states still exist in low-dimensional structures. Previous studies have suggested that phase transitions are impossible in one-dimensional systems [27, 28, 41], and become increasingly less likely as dimensionality further decreases [27, 28, 41, 42], thereby limiting the potential towards the capability improvement of NRERAM.
Experimental effort has been made recently in synthesizing and understanding ferroelectric (FE) nanostructures—e.g., BaTiO3 dots [1], rods [2], wires [3], and nanotubes [4], and Pb(Zr, Ti)O3 thin films [5,6] and nanoparticles [7]. However, it is entirely unknown whether it is possible to increase FE nonvolatile-memory density thousands fold by use of individual nanoparticles [3,8,9]. Furthermore, it is not clear whether these FE nanostructures can continue to be useful and efficient in light of miniaturizing piezoelectric transducers and actuators, ultrasonic devices, and medical imaging detectors [10,11]. These technological uses of enormous importance depend critically on whether ferroelectricity exists in these nanostructures. From a fundamental point of view, ferroelectricity is caused by atomic off-center displacements, resulting from a delicate balance between long-range (LR) Coulomb interaction and short-range (SR) covalent interaction [12]. In nanostructures, both interactions—and thus their balance—are altered with respect to the bulk, since the LR interaction is truncated due to lack of periodicity, while the SR one is significantly modified near the surface boundary. Consequently, it is commonly believed [13-16] that ferroelectricity in nanostructures would disappear entirely (i.e., there is no ferroelectric off-center instability) below a critical size. This belief has recently received support from a theoretical study on BaTiO3 thin films [17]. For FE nanoparticles, while measurements of lattice structures (rather than polarization) are available only at large sizes (˜500 Å, Refs. [14,15]), the critical size of ferroelectricity (if any) is unknown [1-3,7]. In fact, it is not even clear whether there are any ferroelectric displacements in FE dots and/or whether these displacements are aligned to form long-range ferroelectric phases. Similarly, virtually nothing is known about the electrical and mechanical responses of FE nanoparticles to electric fields.